Elliptic curve isogeny class 12996.4-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-12996.4-b
• Conductor: 12996.4
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-2}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).

Elliptic curves in class 12996.4-b over \(\Q(\sqrt{-2}) \)

Isogeny class 12996.4-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12996.4-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( 28 a - 70\) , \( 35 a - 263\bigr] \)
12996.4-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( -197 a + 195\) , \( 519 a - 1900\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph